Thousands of people are at the border with Poland, enduring freezing conditions in the hope of crossing into the European Union.
EU officials have accused Belarus of provoking the crisis to undermine its security, an allegation it denies.
In retaliation, the EU is reportedly planning a fresh package of sanctions.
But on Thursday the country's long-time authoritarian leader Alexander Lukashenko warned: "If they impose additional sanctions on us... we must respond."
"We are heating Europe, and they are threatening us," he said, referring to a Russian gas pipeline that runs through Belarus and into the EU.
"And what if we halt natural gas supplies? Therefore, I would recommend the leadership of Poland, Lithuanians and other empty-headed people to think before speaking," he added.
His comments raised fresh fears amid worsening natural gas shortages and rising prices in Europe.
The EU's economy commissioner Paolo Gentiloni said the bloc "should not be intimidated" by Mr Lukashenko's threats. Exiled Belarusian opposition leader Svetlana Tikhanovskaya, who now lives in Lithuania, accused the president of "bluffing" over his gas ultimatum.
But it is not an empty threat, according to Katja Yafimava, from the Oxford Institute for Energy Studies, who says Mr Lukashenko should be taken seriously.
"The fact that these pipelines are physically on the Belarusian territory gives Belarus a certain leverage. If the EU pushes Belarus too hard, it may act on this threat," Dr Yafimava said.
That could push up gas prices across Europe, including in the UK, she added.
More EU sanctions on Belarus could be introduced as early as Monday. Possible measures include targeting the airport in the capital, Minsk, in an effort to stop international airlines carrying migrants from landing there.